Energy Fluctuations in Slowly Sheared Granular Materials

Here we show the first experimental measurement of the particle-scale energy fluctuations Delta E in a slowly sheared layer of photoelastic disks. Starting from an isotropically jammed state, applying shear causes the shear-induced stochastic strengthening and weakening of particle-scale energies, whose statistics and dynamics govern the evolution of the macroscopic stress-strain curve. We find that the Delta E behave as a temperaturelike noise field, showing a novel, Boltzmann-type, double-exponential distribution at any given shear strain gamma. Following the framework of the soft glassy rheology theory, we extract an effective temperature chi from the statistics of the energy fluctuations to interpret the slow startup shear (shear starts from an isotropically jammed state) of granular materials as an aging process: Starting below one, chi gradually approaches one as gamma increases, similar to those of spin glasses, thermal glasses, and bulk metallic glasses.